List of courts of the United States

The courts of the United States are closely linked hierarchical systems of courts at the federal and state levels. The federal courts form the judicial branch of the federal government of the United States and operate under the authority of the United States Constitution and federal law. The state and territorial courts of the individual U.S. states and territories operate under the authority of the state and territorial constitutions and state and territorial law.

Federal statutes that refer to the "courts of the United States" are referring only to the courts of the federal government, and not the courts of the individual states and counties. Because of the federalist underpinnings of the division between sovereign federal and state governments, the various state court systems are free to operate in ways that vary widely from those of the federal government, and from one another. In practice, however, every state has adopted a division of its judiciary into at least two levels, and almost every state has three levels, with trial courts hearing cases which may be reviewed by appellate courts, and finally by a state supreme court. A few states have two separate supreme courts, with one having authority over civil matters and the other reviewing criminal cases. 47 states and the federal government allow at least one appeal of right from a final judgment on the merits, meaning that the court receiving the appeal must decide the appeal after it is briefed and argued properly. Three states do not provide a right to a first appeal. Rather, they give litigants only a right to petition for the right to have an appeal heard.

...
Wikipedia